Surely 1Sport does not seem to have strong financial backing hence they cannot acquire many sports rights. Eurosport can acquire cricket rights of various boards be it west indies, bangladesh, etc. and they do air cricket matches featuring associate nations. I believe Eurosport has rights of Afghanistan Cricket. Problem is that these rights generate very less revenue and Discovery is not a big broadcaster like star/disney or sony or viacom18 who can sustain such losses, still i believe they need to invest in these apart from niche sports they usually air.
Best option for 1Sport and Eurosport is to have strategic tie up with star sports, sony sports or sports18 so that the channel gets the much needed popular sporting events thus resulting in expansion of viewership. In UK BT Sport recently had such a partnership / merger with Eurosport